The range of an \(\mathrm {SLE}_\kappa \)  process is a random fractal of a.s. Hausdorff dimension \(\min (2,1+\frac{\kappa }{8})\)  [1]},  which is scale invariant and satisfies the so-called domain Markov property: if \(\tau \)  is an a.s. finite stopping time then the law of \(t \mapsto g_\tau (\eta (\tau +t))-W_\tau \)  is that of an \(\mathrm {SLE}_\kappa \)  process in \(\mathbf {H}\)  from 0 to \(\infty \) . One defines \(\mathrm {SLE}_\kappa \)  processes in other simply connected domains as the conformal images of \(\mathrm {SLE}_\kappa \)  in \(\mathbf {H}\) .
